Modeling of the initial stage of secondary flows formation for a fluid, the rheological model of which implies a threshold “addition” of the transverse viscosity factor

Abstract

This paper proposes a rationale for the rheological model of a fluid, which implies a threshold “addition” of the transverse viscosity factor. A modeling of the secondary flows generation in a small neighborhood of the spatial point of the fluid flow region, the mechanical behavior of which is described by the rheological model of this kind, is carried out. The equations of the fluid dynamics for an index arbitrary value in the case of the transverse viscosity power dependence on the modulus exceedance of the strain rate tensor second invariant of the critical level in question are obtained. Interpretation of various scenarios of the flow development in a small neighborhood of the flow region point in which the modulus of the second invariant exceeds the threshold value is presented